This paper presents a new approach to the real time single and multiple target detection and tracking problems with measurement input data. The new approach addresses the measurement uncertainty-of-origin issue by capturing all measurement input data information in the Bayesian conditional probability density function (PDF), used in the recursive propagation of the posterior target detection an...

We investigate the historical volatility of the 100 most capitalized stocks traded in US equity markets. An empirical probability density function (pdf) of volatility is obtained and compared with the theoretical predictions of a lognormal model and of the Hull and White model. The lognormal model well describes the pdf in the region of low values of volatility whereas the Hull and White model ...

A theory of the probability distribution function (PDF) tails of the blob density in plasma edge turbulence is provided. A simplified model of the fast convective radial transport is used. The theoretically predicted PDF tails corroborate earlier measurements of edge transport, further confirming the strongly non-Gaussian feature of edge transport. It is found that increasing the cross sectiona...

Weak lensing measurements are starting to provide statistical maps of the distribution of matter in the universe that are increasingly precise and complementary to cosmic microwave background maps. The probability distribution (PDF) provides a powerful tool to test non-Gausian features in the convergence field and to discriminate the different cosmological models. In this letter, we present a n...

The outage probability of the Switch and Stay Combining/Selection Combining (SSC/SC) combiner output signal at two time instants, in the presence of log-normal fading, is determined in this paper. The probability density function (PDF) of the combiner output signal is derived. Then, the outage probability is numerically calculated using this PDF. The results are shown graphically to compare per...

A technique is presented for representing linear features as probability density functions in 2D or 3D affine space. Two chief advantages of this approach are (1) a unified representation and algebra for manipulating points, lines, and planes, and (2) seamless incorporation of uncertainty information. Applications to Euclidean and non-metric scene reconstruction are presented, with results on i...

We give estimates of the distance between the densities of the laws of two functionals F and G on the Wiener space in terms of the Malliavin-Sobolev norm of F −G. We actually consider a more general framework which allows one to treat with similar (Malliavin type) methods functionals of a Poisson point measure (solutions of jump type stochastic equations). We use the above estimates in order to...

We present an algorithm for grouping families of probability density functions (pdfs). We exploit the fact that under the square-root re-parametrization, the space of pdfs forms a Riemannian manifold, namely the unit Hilbert sphere. An immediate consequence of this re-parametrization is that different families of pdfs form different submanifolds of the unit Hilbert sphere. Therefore, the proble...

Bhat et al. [1] developed an inductive compiler that computes density functions for probability spaces described by programs in a probabilistic functional language. In this work, we implement such a compiler for a modified version of this language within the theorem prover Isabelle and give a formal proof of its soundness w.r.t. the semantics of the source and target language. Together with Isa...